-- | PFOV (Permissive Field of View) clean-room reimplemented based on the algorithm described in <http://roguebasin.roguelikedevelopment.org/index.php?title=Precise_Permissive_Field_of_View>,-- though the general structure is more influenced by recursive shadow casting,-- as implemented in Shadow.hs. In the result, this algorithm is much faster-- than the original algorithm on dense maps, since it does not scan-- areas blocked by shadows.moduleGame.LambdaHack.FOV.Permissive(scan,dline,dsteeper,intersect,debugSteeper,debugLine)whereimportGame.LambdaHack.MiscimportGame.LambdaHack.Utils.AssertimportGame.LambdaHack.FOV.Common-- TODO: Scanning squares on horizontal lines in octants, not squares-- on diagonals in quadrants, may be much faster and a bit simpler.-- Right now we build new view on each end of each visible wall tile-- and this is necessary only for straight, thin, diagonal walls.-- | Calculates the list of tiles, in @Bump@ coordinates, visible from (0, 0).scan::(Bump->Bool)-- ^ clear tile predicate->[Bump]scanisClear=dscan1(((B(0,1),B(999,0)),[B(1,0)]),((B(1,0),B(0,999)),[B(0,1)]))wheredscan::Distance->EdgeInterval->[Bump]dscand(s0@(sl{-shallow line-},sBumps0),e@(el{-steep line-},eBumps))=assert(d>=0&&pe+1>=ps0&&ps0>=0`blame`(d,s0,e,ps0,pe))$ifillegalthen[]elseinside++outsidewhere(ns,ks)=intersectsld(ne,ke)=intersecteld-- Corners are translucent, so they are invisible, so if intersection-- is at a corner, choose pe that creates the smaller view.(ps0,pe)=(ns`div`ks,ne`divUp`ke-1)-- progress interval to check-- A single ray from an extremity produces non-permissive digital lines.illegal=let(n,k)=intersectsl0inns*ke==ne*ks&&(n`elem`[0,k])pd2bump(p,di)=B(di-p,p)bottomRight(p,di)=B(di-p+1,p)inside=[pd2bump(p,d)|p<-[ps0..pe]]outside|isClear(pd2bump(ps0,d))=mscan(Justs0)ps0-- start in light|ps0==ns`divUp`ks=mscan(Justs0)ps0-- start in a corner|otherwise=mscanNothing(ps0+1)-- start in mid-wall-- The current state of a scan is kept in @Maybe Edge@.-- If it's the @Just@ case, we're in a visible interval. If @Nothing@,-- we're in a shadowed interval.mscan::MaybeEdge->Progress->[Bump]mscan(Justs@(_,sBumps))ps|ps>pe=dscan(d+1)(s,e)-- reached end, scan next|not$isClear(pd2bump(ps,d))=-- enter shadow, steep bumpletsteepBump=bottomRight(ps,d)gte=flip$dsteepersteepBump-- sBumps may contain steepBump, but maximal will ignore itnep=maximalgtesBumpsneBumps=addHullgtesteepBumpeBumpsinmscanNothing(ps+1)++dscan(d+1)(s,(dlinenepsteepBump,neBumps))|otherwise=mscan(Justs)(ps+1)-- continue in lightmscanNothingps|ps>ne`div`ke=[]-- reached absolute end|otherwise=-- out of shadow, shallow bump-- the light can be just through a corner of diagonal walls-- and the recursive call verifies that at the same ps coordinateletshallowBump=bottomRight(ps,d)gte=dsteepershallowBumpnsp=maximalgteeBumpsnsBumps=addHullgteshallowBumpsBumps0inmscan(Just(dlinenspshallowBump,nsBumps))ps-- | Create a line from two points. Debug: check if well-defined.dline::Bump->Bump->Linedlinep1p2=assert(uncurryblame$debugLine(p1,p2))$(p1,p2)-- | Compare steepness of @(p1, f)@ and @(p2, f)@.-- Debug: Verify that the results of 2 independent checks are equal.dsteeper::Bump->Bump->Bump->Booldsteeperfp1p2=assert(res==debugSteeperfp1p2)$reswhereres=steeperfp1p2-- | The Y coordinate, represented as a fraction, of the intersection of-- a given line and the line of diagonals of squares at distance-- @d@ from (0, 0).intersect::Line->Distance->(Int,Int)intersect(B(x,y),B(xf,yf))d=assert(allB(>=0)[x,y,xf,yf])$((1+d)*(yf-y)+y*xf-x*yf,(xf-x)+(yf-y)){-
Derivation of the formula:
The intersection point (xt, yt) satisfies the following equalities:
xt = 1 + d - yt
(yt - y) (xf - x) = (xt - x) (yf - y)
hence
(yt - y) (xf - x) = (xt - x) (yf - y)
yt (xf - x) - y xf = xt (yf - y) - x yf
yt (xf - x) - y xf = (1 + d) (yf - y) - yt (yf - y) - x yf
yt (xf - x) + yt (yf - y) = (1 + d) (yf - y) - x yf + y xf
yt = ((1 + d) (yf - y) + y xf - x yf) / (xf - x + yf - y)
General remarks:
A square is denoted by its bottom-left corner. Hero at (0, 0).
Order of processing in the first quadrant is
9
58
247
@136
so the first processed square is at (0, 1). The order is reversed
wrt the restrictive shadow casting algorithm. The line in the curent state
of mscan is not the steep line, but the shallow line,
and we start scanning from the bottom right.
The Point coordinates are cartesian. The Bump coordinates are cartesian,
translated so that the hero is at (0, 0) and rotated so that he always
looks at the first quadrant. The (Progress, Distance) cordinates
are mangled and not used for geometry.
-}-- | Debug functions for PFOV:-- | Debug: calculate steeper for PFOV in another way and compare results.debugSteeper::Bump->Bump->Bump->BooldebugSteeperf@(B(xf,yf))p1@(B(x1,y1))p2@(B(x2,y2))=assert(allB(>=0)[xf,yf,x1,y1,x2,y2])$let(n1,k1)=intersect(p1,f)0(n2,k2)=intersect(p2,f)0inn1*k2<=k1*n2-- | Debug: checks postconditions of borderLine.debugLine::Line->(Bool,String)debugLineline@(B(x1,y1),B(x2,y2))|not(allB(>=0)[x1,y1,x2,y2])=(False,"negative coordinates: "++showline)|y1==y2&&x1==x2=(False,"ill-defined line: "++showline)|x2-x1==-(y2-y1)=(False,"diagonal line: "++showline)|crossL0=(False,"crosses diagonal below 0: "++showline)|crossG1=(False,"crosses diagonal above 1: "++showline)|otherwise=(True,"")where(n,k)=intersectline0(q,r)=ifk==0then(0,0)elsen`divMod`kcrossL0=q<0-- q truncated toward negative infinitycrossG1=q>=1&&(q>1||r/=0)